{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2-多变量线性回归\n",
    "\n",
    "##  案例：假设你现在打算卖房子，想知道房子能卖多少钱？\n",
    "###  我们拥有房子面积和卧室数量以及房子价格之间的对应数据： ex1data2.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 读取文件"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "   size  bedrooms   price\n0  2104         3  399900\n1  1600         3  329900\n2  2400         3  369000\n3  1416         2  232000\n4  3000         4  539900",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>size</th>\n      <th>bedrooms</th>\n      <th>price</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2104</td>\n      <td>3</td>\n      <td>399900</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1600</td>\n      <td>3</td>\n      <td>329900</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2400</td>\n      <td>3</td>\n      <td>369000</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1416</td>\n      <td>2</td>\n      <td>232000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>3000</td>\n      <td>4</td>\n      <td>539900</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('ex1data2.txt', names=['size', 'bedrooms', 'price'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.特征归一化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize_feature(data):\n",
    "    return (data - data.mean()) / data.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = normalize_feature(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "       size  bedrooms     price\n0  0.130010 -0.223675  0.475747\n1 -0.504190 -0.223675 -0.084074\n2  0.502476 -0.223675  0.228626\n3 -0.735723 -1.537767 -0.867025\n4  1.257476  1.090417  1.595389",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>size</th>\n      <th>bedrooms</th>\n      <th>price</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.130010</td>\n      <td>-0.223675</td>\n      <td>0.475747</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>-0.504190</td>\n      <td>-0.223675</td>\n      <td>-0.084074</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.502476</td>\n      <td>-0.223675</td>\n      <td>0.228626</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-0.735723</td>\n      <td>-1.537767</td>\n      <td>-0.867025</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.257476</td>\n      <td>1.090417</td>\n      <td>1.595389</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot.scatter('size', 'price', label='size')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot.scatter('bedrooms', 'price', label='bedrooms')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 添加全为1的列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "   ones      size  bedrooms     price\n0     1  0.130010 -0.223675  0.475747\n1     1 -0.504190 -0.223675 -0.084074\n2     1  0.502476 -0.223675  0.228626\n3     1 -0.735723 -1.537767 -0.867025\n4     1  1.257476  1.090417  1.595389",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>ones</th>\n      <th>size</th>\n      <th>bedrooms</th>\n      <th>price</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>0.130010</td>\n      <td>-0.223675</td>\n      <td>0.475747</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>-0.504190</td>\n      <td>-0.223675</td>\n      <td>-0.084074</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1</td>\n      <td>0.502476</td>\n      <td>-0.223675</td>\n      <td>0.228626</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1</td>\n      <td>-0.735723</td>\n      <td>-1.537767</td>\n      <td>-0.867025</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1</td>\n      <td>1.257476</td>\n      <td>1.090417</td>\n      <td>1.595389</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.insert(0, 'ones', 1)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 构造数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.iloc[:, 0:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "   ones      size  bedrooms\n0     1  0.130010 -0.223675\n1     1 -0.504190 -0.223675\n2     1  0.502476 -0.223675\n3     1 -0.735723 -1.537767\n4     1  1.257476  1.090417",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>ones</th>\n      <th>size</th>\n      <th>bedrooms</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>0.130010</td>\n      <td>-0.223675</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>-0.504190</td>\n      <td>-0.223675</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1</td>\n      <td>0.502476</td>\n      <td>-0.223675</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1</td>\n      <td>-0.735723</td>\n      <td>-1.537767</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1</td>\n      <td>1.257476</td>\n      <td>1.090417</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data.iloc[:, -1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "0    0.475747\n1   -0.084074\n2    0.228626\n3   -0.867025\n4    1.595389\nName: price, dtype: float64"
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 将dataframe转成数组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(47, 3)"
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(47,)"
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = y.reshape(47, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(47, 1)"
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(X, y, theta):\n",
    "    inner = np.power(X @ theta - y, 2)\n",
    "    return np.sum(inner) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.zeros((3, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_init = costFunction(X, y, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48936170212765967\n"
     ]
    }
   ],
   "source": [
    "print(cost_init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 梯度下降函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, theta, alpha, iters, isprint=False):\n",
    "    costs = []\n",
    "\n",
    "    for i in range(iters):\n",
    "        theta = theta - (X.T @ (X @ theta - y)) * alpha / len(X)\n",
    "        cost = costFunction(X, y, theta)\n",
    "        costs.append(cost)\n",
    "\n",
    "        if i % 100 == 0:\n",
    "            if isprint:\n",
    "                print(cost)\n",
    "\n",
    "    return theta, costs"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 不同alpha下的效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "candinate_alpha = [0.0003, 0.003, 0.03, 0.0001, 0.001, 0.01, 0.5, 1]\n",
    "iters = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "for alpha in candinate_alpha:\n",
    "    _, costs = gradientDescent(X, y, theta, alpha, iters)\n",
    "    ax.plot(np.arange(iters), costs, label=alpha)\n",
    "    ax.legend()\n",
    "\n",
    "ax.set(xlabel='iters',\n",
    "       ylabel='cost',\n",
    "       title='cost vs iters')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
